LT8: Matching
Sam Marden
s.h.marden@lse.ac.uk
Introduction
Describe the intuition behind matching estimators. Be concise.
Suppose you have a sample of 100,000 prospective voters, with
data on age, gender, party affiliation, county of residence, and
whether or not an individual voted in the last elections. Ten
thousand of these individuals were reached by telephone and
heard a short message from a non-partisan agency regarding the
importance of voting. The aim of the message was to improve
voter turn out. Explain in no more than three sentences how one
would use a matching estimator to estimate the effect of the
calls. Note, you do not need to provide technical details (that
comes next week), but a clear and intuitive explanation of how
you would construct the matching estimator.
What do we expect the effect of piped
water to be?
Is it likely to be heterogenous?
What do we expect the effect of piped
water to be?
Piped water  Fewer Pathogens  Less Disease
Is it likely to be heterogenous with income?
Maybe, Piped Water ≠ Clean Water
• interacts with other inputs e.g. storage of water, access
to medical facilities etc, so increases/decreases the MB
of these inputs
• If other inputs have an income elasticity ≠ 0 then
different effects on rich and poor
Picture of a water pipe and child for no
reason
Do the propensity scores look
plausible?
Now we’ve done our propensity
regression what do JR do with them?
Now we’ve done our propensity
regression what do JR do with them?
1. Compute the fitted values: this gives the probability
of being in the treatment group conditional on
observables: p(xi)=Prob(T=1|xi)
2. For each observation in the treatment group find the
five nearest neighbours i.e. the ones that minimise
|p(xi)-p(xj)|
3. Throw out observations in the treatment group which
don’t have at least 5 neighbours that have with
conditional treatment probabilities within 3.2p.p of
the treated observation
4. For those that remain. Take an average of the five
nearest neighbours and call this the counterfactual.
What does figure 1 tell us?
What does figure 1 tell us?
• Treated individuals have
higher propensity scores.
• Common support across
much of the distribution
• Not too many control
observations with very
high scores.
• Consequently 650
treated observations
dropped.
What are the key results of the paper?
How different are the Matching
Results from the OLS estimates?
They are buried in the text but they are very similar
when run on sample of common support ASPSM.
We don’t get the other results.
• Not really surprising
– ‘Same’ identification assumption
– But PSM allows for non-linear relationship between
controls and y
– If the relationship between controls and y is linear
then results should be the same but less precisely
estimated
– Less precision comes partly from weighting
How different are the Matching
Results from the OLS estimates?
Which un-observables may be biasing
the results?
Which un-observables may be biasing
the results?
• We need to worry about unobservables that
are correlated with diarrhea, corellated with
the presence of a water pipe, and not
perfectly correlated with other observables
• This is the same condition as for OLS
• E.g. preferences for hygiene reduce the
incidence of diarrhea and would make people
want to live near a water pipe.
What are the key policy implications
for this paper?
What are the key policy implications
for this paper?
• Water pipes are sweet
• Poor people are dirty may need help
maximising the benefits of cleaner water and
to be provided with other complementary
inputs
• There may be complementarities between
knowledge, other investments and access to
piped water
Describe an experiment that you
would like to run.